Expansion for the solutions of the Bogomolny equations on the torus

Details Expansion for the solutions of the Bogomolny equations on the torus Expansion for the solutions of the Bogomolny equations on the torus

2004-04-02

arxiv.org/abs/hep-th/0404022v2

JHEP 0407 (2004) 008

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 8 figures, slightly revised version as published in JHEP

Scientific paper

10.1088/1126-6708/2004/07/008

We show that the solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus, can be expanded in powers of a quantity epsilon measuring the departure of the area from the critical area. This allows a precise determination of the shape of the solutions for all magnetic fluxes and arbitrary position of the Higgs field zeroes. The expansion is carried out to 51 orders for a couple of representative cases, including the unit flux case. We analyse the behaviour of the expansion in the limit of large areas, in which case the solutions approach those on the plane. Our results suggest convergence all the way up to infinite area.

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